For the first question you have to be careful. You know that g=GM/r^2, it is proportional to M/r^2. You know that volume is proportional to r^3 (V=4/3pir^3) Hence if the diameter increases by 100x, the radius also does, and the volume increases by 10^6. To keep the density constant the mass must also increase by 10^6 since density=mass/vol. Now since g is proportional to M/r^2. r has increased by 100^2 and M has increased by 10^6. Therefore g must have increased by 100x. Therefore g on the surface of the star is 100x8=800NKg^-1.

For the second question, weight is proportional to the gravitational force on that object. Hence if R increases to 2R then the force decreases by 4, but since the mass increases by two, this increases the force on the mass by a factor of 2. 2x1/4 = 1/2 therefore the weight halves to W/2.